Hydraulics and Fluid Mechanics in ME
The loss of head due to viscosity for laminar flow in pipes is (where d = Diameter of pipe, l = Length of pipe, v = Velocity of the liquid in the pipe, μ = Viscosity of the liquid, and w = Specific weight of the flowing liquid)

32μvl/wd²
4μvl/wd²
16μvl/wd²
8μvl/wd²

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Hydraulics and Fluid Mechanics in ME
For similarity, in addition to models being geometrically similar to prototype, the following in both cases should also be equal

all the four ratios of inertial force to force due to viscosity, gravitation, surface tension, and elasticity
ratio of inertial force to force due to gravitation
ratio of inertial force to force due to surface tension
ratio of inertial force to force due to viscosity

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Hydraulics and Fluid Mechanics in ME
The discharge through a wholly drowned orifice is given by (where H1 = Height of water (on the upstream side) above the top of the orifice, H2 = Height of water (on the downstream side) above the bottom of the orifice, and H = Difference between two water levels on either side of the orifice)

Q = Cd × b (H2 - H1) × √(2gh)
Q = Cd × bH × √(2gh)
Q = Cd × bH₁ × √(2gh)
Q = Cd × bH2 × √(2gh)

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